Geotechnical Engineering

DHARM

530 GEOTECHNICAL ENGINEERING

H = 3.6 m φ = 20° β = 20° α = 81° δ = 12° ψ = α – δ = 69°
Since β = φ, the special case of Rebhann’s construction for this condition is applied. The
triangle CGL is constructed from any arbitrary point C.

Pa =

1

2

1

2

γψx^22 .sin =× ×18 9. (. ) sin3 85 69 ° = 131 kN/m. run

The rupture surface cannot be located in this case.

b= 20°

a= 81°

f= 20°

3.6 m

Wall

9°

x = 3.85 m

f–line

M

y= 69°

3.6 m

L yad= ( – ) = (81° — 12°) = 69°

G

C

Fig. 13.66 Special case of Rebhann’s construction when β = φ (Ex. 13.21)

Example 13.22: A masonry wall with vertical back has a backfill 5 m behind it. The ground
level is horizontal at the top and the ground water table is at ground level. Calculated the
horizontal pressure on the wall using Coulomb’s earth pressure theory. Assume the unit weight
of saturated soil is 15.3 kN/m^3. Cohesion = 0. φ = 30°. Friction between wall and earth = 20°.

(S.V.U.—B.E., (N.R.)—Sep., 1968)

H = 5 m c = 0 φ = 30° δ = 20° γsat = 15.3 kN/m^3

Ka = sin ( )

sin .sin( ) sin( ).sin( )

sin( ).sin( )

2

2

2

1

αφ

ααδ φδ φβ

αδ αβ

+

−+ +−

−+

L

N

M

M

O

Q

P

P

since α = 90° and β = 0° in this case,

Ka =

cos

cos sin( ).sin

cos

2

2

1

φ

δ φδ φ

δ

+ +

L

N

M

M

O

Q

P

P

=

cos

cos sin .sin

cos

.

2

2

30

20 1^5030

20

0132

°

°+

°°

°

L

N

M

M

O

Q

P

P

=